It is one of the many Carex species, probably from section Griseae in the keys.

Thanks esh & bagsmom! I figured that would be the only way to keep that stuff outta the beds. I was hoping someone might know of something that would kill the grass without hurting my plants. As if!! I know its asking alot but I am so frustrated. GGG, it sounds like you are describing my sisters yard who has the zoysia. I knew that was its nature but since so many people have it they would have some easy way to control it. grrrrrr Thanks again everyone!!

This is an excellent question with few good answers. The time to deal with the compaction issue is before you plant. Once the plants, especially trees, are in the ground, your options are limited. That is one of the biggest reasons why I am no fan of lasagna gardening. Once everything is in the ground, it is a little late to be going back to what should have been done in the first place. However, not all is lost. A reasonably easy solution to compaction problems is raised beds. Although not very common in Iowa, in places where bedrock is near the surface, you have little other choice if you want to garden. Of course, where bedrock is deep but compaction is a problem, the old solution favored by the British was to double dig their garden beds. In other words, they would remove the soil a full spade depth, set it aside and dig yet another full spade depth. Amendments were added as the bed was refilled. This is a tried and true method that works extremely well. Unfortunately, it is also backbreaking work. Most people are unwilling to expend this much energy and are looking for easier methods. Hence, the popularity of lasagna gardening; which is actually only a slight modification of Ruth Stouts method written about decades before a slick marketing name was given to it. Hey, if you are currently using the lasagna method and are pleased with the results, have at it. It is certainly much better than not gardening at all. However, be honest with yourself and realize that it does have limitations. It is not a cure-all. Quite frankly, one should have enough common sense to realize that if it sounds too good to be true  it probably is. Soil compaction is not eliminated; it is only masked to the uninformed. The way that I addressed the issue of soil compaction was to deal with it when my house was being built  a narrow window of opportunity not afforded to most of us very often. I subsoiled my entire yard to a depth of about 16 inches. (Make sure you call for the utilities to be located, first.) I then incorporated truckloads of compost into the soil as deeply as possible with a tractor-mounted rototiller. And then, most importantly, I kept all heavy vehicle traffic OFF. As I built my garden beds, I incorporated even more compost into those areas and now walk only on the paths. As to the original question of this thread: At my older homes, I eliminated grass by cutting it off with a sharp spade (a sod cutter would work well) and then threw the sod into the bottom of the beds that I was double digging. I further amended nasty, yellow clay by using an old Karen Strohbeen garden soil formula: 30% soil, 30% coarse sand & 30% compost. The soil was tilled and the results were wonderful. I gained supplementary benefits of modified raised beds due to the additional materials and air space. On existing beds, whenever I lifted plants for dividing and/or replacement, I took the opportunity to dig down and create "Karen Strohbeen soil". Of course, at times I hit big tree roots so you just do the best you can. I realize that there are many more ways to do things than the ones I have chosen. Also there are many, many other extenuating factors to consider. For one, I am a big strong guy. If I asked my wife to double dig a new garden bed, she would probably use the spade to double whack me! My preference now is to use my 40 hp tractor to pull a subsoiler. Not all people have a tractor. Some have health issues that demand they use less strenuous methods. For many of these people, lasagna gardening can provide an attractive option. However, sometimes the claims I have heard people making, approach that of a snake oil salesman. Life is full of compromises and tradeoffs  and this is just another example. Every coin has two sides. IronBelly

Maybe I'm being naive, but is it possible to pull the grass and weeds for now? That's what I do.